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|---|---|---|
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Solve a + 3a = -6a - 2x - 5 for a in terms of x.
| \(\frac{5}{14}\)x + \(\frac{9}{14}\) | |
| -\(\frac{2}{5}\)x - \(\frac{4}{5}\) | |
| -\(\frac{5}{7}\)x - \(\frac{5}{7}\) | |
| \(\frac{1}{8}\)x - \(\frac{5}{8}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
a + 3x = -6a - 2x - 5
a = -6a - 2x - 5 - 3x
a + 6a = -2x - 5 - 3x
7a = -5x - 5
a = \( \frac{-5x - 5}{7} \)
a = \( \frac{-5x}{7} \) + \( \frac{-5}{7} \)
a = -\(\frac{5}{7}\)x - \(\frac{5}{7}\)
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
division |
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pairs |
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addition |
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exponents |
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
Which of the following statements about math operations is incorrect?
you can add monomials that have the same variable and the same exponent |
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all of these statements are correct |
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you can subtract monomials that have the same variable and the same exponent |
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you can multiply monomials that have different variables and different exponents |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.
Solve for x:
x2 + 7x - 18 = 2x - 4
| 2 or -7 | |
| 4 or -7 | |
| 7 or -6 | |
| -2 or -5 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
x2 + 7x - 18 = 2x - 4
x2 + 7x - 18 + 4 = 2x
x2 + 7x - 2x - 14 = 0
x2 + 5x - 14 = 0
Next, factor the quadratic equation:
x2 + 5x - 14 = 0
(x - 2)(x + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 2) or (x + 7) must equal zero:
If (x - 2) = 0, x must equal 2
If (x + 7) = 0, x must equal -7
So the solution is that x = 2 or -7
Which of the following statements about a parallelogram is not true?
the perimeter of a parallelogram is the sum of the lengths of all sides |
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a parallelogram is a quadrilateral |
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the area of a parallelogram is base x height |
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opposite sides and adjacent angles are equal |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).